With a pair of standard dice of one shade, the face of each six-sided die contains one of six numbers ranging in value from 1 through 6, usually represented by furrowed dots commonly referred to as pips. The number of pips on one side of a die, added to the number of pips on the opposite side, will always display the sum of seven. In any kind of dice game, both dice are shaken together and rolled out on either a table or a playing board. The number of pips that appear on the upper face of each die, added together, gives one of eleven numerical sums, the value of which determines the outcome of a dice game.
Since there are six ways each of two six-sided dice can turn up in a dice roll, 6 (die one).times.6 (die two), thirty-six possible numerical combinations of two dice will give the eleven numerical sums ranging from two through twelve as shown in Table 1.
TABLE 1 __________________________________________________________________________ COMBINATIONS OF TWO NUMBERED DICE ELEVEN SUMS OF TWO DICE THIRTY-SIX POSSIBLE NUMERICAL SUMS __________________________________________________________________________ 2 1 + 1 (Snake Eyes) 3 1 + 2, 2 + 1 4 1 + 3, 3 + 1, 2 + 2 5 1 + 4, 4 + 1, 2 + 3, 3 + 2 6 Nine 1 + 5, 5 + 1, 2 + 4, 4 + 2, 3 + 3 7 Group 1 + 6, 6 + 1, 2 + 5, 5 + 2, 3 + 4, 4 + 3 8 Sums 2 + 6, 6 + 2, 3 + 5, 5 + 3, 4 + 4 9 3 + 6, 6 + 3, 4 + 5, 5 + 4 10 4 + 6, 6 + 4, 5 + 5 11 5 + 6, 6 + 5 12 6 + 6 (Box Cars) __________________________________________________________________________
Examination of Table 1, clearly shows how many identical sums are possible within nine separate collective groups of sums, ranging in value from three to eleven. With a pair of standard dice of one shade, the identical sums within any one of the nine groups of sums are observed one way, collectively, when the dice are rolled. Even though, there are thirty-six numerical combinations that can be rolled, only eleven sums, ranging in value from two to twelve are observed. For example, the six ways number seven can turn up in a dice roll are: 1 (die one)+6 (die two); 6 (die one)+1 (die two); 2 (die one)+5 (die two); 5 (die one)+2 (die two); 3 (die one)+4 (die two) and 4 (die one)+3 (die two). However, with a pair of standard one color dice, it is impossible to visually discern the three pairs of numbers on one die from the three pairs of numbers on the companion die in any of the six rolled combinations of dice to obtain the sum of seven. Even though there are six separate ways number seven can turn up in a dice roll, there are no games that can be played with a pair of standard one color numbered dice, to visually differentiate the six possible ways to obtain seven, or for that matter, any of the combinations for the numerical sums of three, four, five, six, eight, nine, ten or eleven.
Since the two dice in a pair of standard dice are of the same color, it is impossible for game participants to visually differentiate each of the thirty-six rolled sums of the two dice that collectively display the eleven numerical sums, ranging in value from two through twelve. Without the ability to visually differentiate these thirty-six possible numerical sums of the two dice, all current dice related games using a pair of one color dice, incorporating various playing boards, playing cards or a combination thereof, are limited to only eleven visually discernable numerical sums, each of which turns up in varying odds.
The probability, percent (P) and odds for the eleven numerical sums, ranging in value from two to twelve, observed with a pair of standard one color dice, are summarized in Table 2.
TABLE 2 ______________________________________ NUMBER OF ROLLED WAYS (COM- PROBABILITY SUM BINATIONS) (P) % (P) ODDS ______________________________________ 2 1 1/36 3 35 to 1 3 2 1/18 6 17 to 1 4 3 1/12 8 11 to 1 5 4 1/9 11 8 to 1 6 5 1/7 14 6 to 1 7 6 1/6 17 5 to 1 8 5 1/7 14 6 to 1 9 4 1/9 11 8 to 1 10 3 1/12 8 11 to 1 11 2 1/18 6 17 to 1 12 1 1/36 3 35 to 1 ______________________________________
Color or symbol coding each of six or more numbered or unnumbered faces on one die or multiples of such dice, as a means to develop specific dice related games, incorporating playing boards, playing cards or a combination thereof, is widely exemplified in the patent literature, with specific references cited in U.S. Pat. Nos. 1,481,628; 1,631,505; 2,526,300; 2,992,652; 3,055,662; 3,433,483; 3,709,498; 3,977,679; 4,015,850; 4,046,381; 4,261,574; 4,335,879; 4,346,900 and 4,436,306. However, no where in the patents cited or for that matter in the general patent literature, has it been found or is it apparent to one skilled in the art, that a visual system was ever developed to show how the identical sums of two numbered dies are visually differentiated one from the other.